SOLUTION: Hi. I continually have difficulty solving distance problems involving multiple variables. Here is my question. Thank you so much. A railroad and a highway intersect at right an

Question 715206: Hi. I continually have difficulty solving distance problems involving multiple variables. Here is my question. Thank you so much.
A railroad and a highway intersect at right angles. A train is 10 miles from the intersection at the same moment that a car is 6 miles from the intersection. Both are traveling at 30 mph. How long until they are 4 miles apart?
There are two answers:
First time = _______ minutes
Second time = ______ minutes
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A railroad and a highway intersect at right angles. A train is 10 miles from the intersection at the same moment that a car is 6 miles from the intersection. Both are traveling at 30 mph. How long until they are 4 miles apart?
----
Draw the picture so you can see what is happening with the distances:
Train DATA:
rate = 30 mph ; time = t hours ; distance = 30t miles
---
Car DATA:
rate = 30 mph ; time = t hour ; distance = 30t miles
-----
Distance train is from the intersection: 10-30t miles
Distance car is from the intersection: 6-30t miles
-----
Use Pythagoras:
(10-30t)^2 + (6-30t)^2 = 4^2
100 - 600t + 900t^2 + 36 - 360t + 900t^2 = 16
-------
1800t^2 -960t + 120 = 0
-------
Divide thru by 120 to get:
15t^2 - 8t + 1 = 0
(3t-1)(5t-1) = 0
----
t = 1/3 hr = 20 min
Or
t = 1/5 hr = 12 min
====================
Cheers,
Stan H.
====================
RELATED QUESTIONS
Hi. My name is Allen and I've been having difficulty solving these log problems. Here is... (answered by josmiceli)

hi, I'm Sarah and i'm in 10th grade taking algebra 2, but i'm also taking an SAT prep... (answered by hayek,josmiceli)

Hello! I am reviewing my Algebra for this year and I am having difficulty solving this... (answered by bucky)

I am learning chapter 3 section 6, which is on "steps for solving word problems". The... (answered by ankor@dixie-net.com)

Suppose the population density in the Wichita, Kansas, area is related to the distance... (answered by jim_thompson5910)

I'm pretty sure this would be considered as an expression involving variables,etc. I have (answered by elima)

HI, I have been given a question on Factorising Quadratic Expressions, and need to put... (answered by Cromlix)

I am homeschooled with the School of Tomorrow, and am struggling with solving word... (answered by stanbon)

My question is in reference to one involving "Solving systems of linear equations by the... (answered by Earlsdon)